Fig. 2. Relation of antenna : rectenna areas. with K=20 km4; Woodcock (23) discusses a system with K=150 km4; while NASA's Reference System has K=62 km4 (see Fig. 2). The actual sizes of antenna and rectenna are determined by their relative costs, so that the total cost is a minimum. Different studies have calculated different optima, but NASA's Reference System specifies a 1 km diameter antenna with a 10 km diameter rectenna, for an overall reception of 88%, and an overall transmission efficiency of 63%. The total cost of the transmitting antenna (including transportation) is approximately $2600 m, or an average of $3300/m2. However, not all of this average cost depends on the area of the antenna. Only a portion of the cost—that for the structure, subarrays, waveguides, busses and some control systems — increases with increasing antenna area, while the cost of klystrons, power conditioning and most of the thermal control systems do not. In 1977 Woodcock (23) estimated the incremental cost for the antenna as $600/m2 out of an average of $2500/m2. The proportionate figure today, in round figures, would be $800/m2 out of the average $3300/m2. However, using figures from NASA's Reference Design and the more detailed figures in Denman et al. (13), and rounding to allow for disagreements between the figures, we can derive the rather more conservative figure of $1000/m2 for the incremental cost, giving the equation: where Ca represents the cost of the antenna in $ million, and Aa represents the area of the antenna in km2. By combining these costs with Figs 1 and 2, we obtain the relative costs of antenna and rectenna (Fig. 3). Finally, by combining these costs, we obtain curves showing the minimum cost configurations for the antenna plus rectenna system (Fig. 4). 5. CONCLUSIONS There are two points to note in particular: first, using these equations, NASA's Reference Design does not appear to be optimal for the case of the land rectenna.
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